1944edo: Difference between revisions
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== Theory == | |||
1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1|7]] is about halfway between its steps. In the 5-limit, it [[tempering out|tempers out]] the [[luna comma]], {{monzo| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament, providing a tuning close to [[POTE]] tuning. | |||
In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|1944}} | |||
=== Subsets and supersets === | |||
Since 1944 factors into {{factorization|1944}}, 1944edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
per 8ve | |- | ||
!Generator | ! Periods<br />per 8ve | ||
! Generator* | |||
!Cents | ! Cents* | ||
! Associated<br />ratio* | |||
!Associated ratio | ! Temperaments | ||
!Temperaments | |- | ||
| 1 | |||
| 313\1944 | |||
| 193.210 | |||
| 262144/234375 | |||
| [[Luna]] (5-limit) | |||
|- | |||
| 24 | |||
| 944\1944<br />(53\1944) | |||
| 582.716<br />(32.716) | |||
| 7/5<br />(?) | |||
| [[Chromium]] (1944d) | |||
|- | |- | ||
|72 | | 72 | ||
|892\1944 | | 892\1944<br />(1\1944) | ||
(1\ | | 550.617<br />(0.617) | ||
|550.617 | | 73205/53248<br />(?) | ||
(0.617) | | [[Jamala]] | ||
|73205/53248 | |||
(?) | |||
|[[Jamala]] | |||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||